In general the entropy function is based upon the lattice. For
example, in the case of the simple one dimensional lattice with
velocities \( \mathbf {v} = (-c,0,c)\)  and corresponding populations \(\mathbf {f} = (f_-,f_0,f_+)\)  an explicit Boltzmann style entropy
function is known [1]}:
\(S(\mathbf {f}) = -f_-\log (f_-) - f_0\log (f_0/4) - f_+\log (f_+).\) 
